Interference channel capacity region for randomized fixed-composition codes

The randomized fixe-composition with optimal decoding error exponents are studied \cite{Raul_ISIT,Raul_journal} for the finite alphabet interference channel (IFC) with two transmitter-receiver pairs. In this paper we investigate the capacity region of the randomized fixed-composition coding scheme. A complete characterization of the capacity region of the said coding scheme is given. The inner bound is derived by showing the existence of a positive error exponent within the capacity region. A simple universal decoding rule is given. The tight outer bound is derived by extending a technique first developed in \cite{Dueck_RC} for single input output channels to interference channels. It is shown that even with a sophisticated time-sharing scheme among randomized fixed-composition codes, the capacity region of the randomized fixed-composition coding is not bigger than the known Han-Kobayashi \cite{Han_Kobayashi} capacity region. This suggests that the average behavior of random codes are not sufficient to get new capacity regions.